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3 years ago

Determine whether the relation represents a function. If it is a function, state the domain and range.

Mathematics

1 answer:

oee [108]3 years ago

3 0

Answer: Yes it is a function

Step-by-step explanation:

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How do you solve this do i need to plpug in the formula

Sergeeva-Olga [200]

Answer:

B. -2, 2

Step-by-step explanation:

Apparently, we're to presume that f(x) is the line that is graphed. It has a y-intercept of +1 and a slope (rise/run) of 1/2. Its equation is ...

f(x) = 1/2x +1

If we want points of intersection, we want to solve the equation f(x) = g(x) for the values of x that make it so.

1/2x +1 = √(x +2)

Squaring both sides, we get ...

1/4x² +x + 1 = x +2

1/4x² = 1 . . . . . . . . . . . . subtract x+1 from both sides

x² -4 = 0 . . . . . . . . . . multiply by 4, subtract 4

(x -2)(x +2) = 0 . . . . factor the difference of squares

x = -2, 2 . . . . . . . . . values of x that make the factors zero

The solutions to f(x) = g(x) are x = -2 and x = 2.

_____

<em>Additional comment</em>

The attached graph shows the x- and y-values at the points of intersection. The solutions to f(x) = g(x) are only the x-values, -2 and 2.

The square of (ax +b) is ...

(ax +b)² = a²x² +2abx +b²

The point-slope equation of a line is ...

y = mx + b . . . . . line with slope m and y-intercept b

3 0

2 years ago

A bag contains 40 cards of five different colors. The probability of selecting each color is listed in the chart.

inna [77]

Answer:

Step-by-step explanation:

5 0

3 years ago

Consider the region bounded by the curves y=|x^2+x-12|,x=-5,and x=5 and the x-axis

Tasya [4]

Ooh, fun

what I would do is to make it a piecewise function where the absolute value becomse 0

because if you graphed y=x^2+x-12, some part of the garph would be under the line
with y=|x^2+x-12|, that part under the line is flipped up

so we need to find that flipping point which is at y=0
solve x^2+x-12=0
(x-3)(x+4)=0
at x=-4 and x=3 are the flipping points

we have 2 functions, the regular and flipped one
the regular, we will call f(x), it is f(x)=x^2+x-12
the flipped one, we call g(x), it is g(x)=-(x^2+x-12) or -x^2-x+12
so we do the integeral of f(x) from x=5 to x=-4, plus the integral of g(x) from x=-4 to x=3, plus the integral of f(x) from x=3 to x=5

A.
$\int\limits^{-5}_{-4} {x^2+x-12} \, dx + \int\limits^{-4}_3 {-x^2-x+12} \, dx + \int\limits^3_5 {x^2+x-12} \, dx$

B.
sepearte the integrals
$\int\limits^{-5}_{-4} {x^2+x-12} \, dx = [\frac{x^3}{3}+\frac{x^2}{2}-12x]^{-5}_{-4}=(\frac{-125}{3}+\frac{25}{2}+60)-(\frac{64}{3}+8+48)=\frac{23}{6}$

next one
$\int\limits^{-4}_3 {-x^2-x+12} \, dx=-1[\frac{x^3}{3}+\frac{x^2}{2}-12x]^{-4}_{3}=-1((-64/3)+8+48)-(9+(9/2)-36))=\frac{343}{6}$

the last one you can do yourself, it is $\frac{50}{3}$
the sum is $\frac{23}{6}+\frac{343}{6}+\frac{50}{3}=\frac{233}{3}$

so the area under the curve is $\frac{233}{3}$

6 0

2 years ago

HELP PLEASE!! 30 POINTS!!

agasfer [191]

Your answer is A
hope this helped
to get this answer you multiply 475 by 1.75% and then you get 8.31

4 0

3 years ago

Read 2 more answers

5. Car rental company A charges $30 a days and

olga nikolaevna [1]

Answer:

Step-by-step explanation: